Quantum Computing for Quantum Chemistry A Tensor Hypercontraction approach to Linear Combination of Unitaries

Brahmachari, Aritra Sankar (2025) Quantum Computing for Quantum Chemistry A Tensor Hypercontraction approach to Linear Combination of Unitaries. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Aritra Sankar Brahmachari (20MS082)) 20MS082_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

Quantum computing offers a way to overcome the exponential complexity associated with many-body quantum simulation. Advent of fault tolerant quantum computers could revolutionize fields like computational chemistry and materials science, where conventional approaches struggle to accurately capture strong electron correlations. Linear Combination of Unitaries (LCU) has emerged as a potent technique for encoding Hamiltonians on quantum computers, enabling efficient simulation and electronic structure calculations in quantum chemistry. This work begins with a review the development of the various LCU decompositions over the years, starting from the underlying motivation that led to their introduction. We thereafter introduce the Majorana Tensor Decomposition (MTD), a unifying framework for existing LCUs and introduce novel decompositions using low-rank tensor factorizations. We benchmark a large set of LCU techniques on small molecular systems and study their scaling behaviour on hydrogen chains. We also introduce the Block Invariant Symmetry Shift (BLISS) technique which lowers the circuit cost of LCUs by modifying the Hamiltonian action on only the undesired electron-number subspaces. We apply BLISS to industrially-relevant homogeneous catalysts and demonstrate that this novel method can substantially reduce both the spectral range of the modified Hamiltonian and the 1-norms of Pauli and fermionic LCUs such as Tensor Hypercontraction (THC). Notably, we show that BLISS can reduce the circuit cost of THC encoding by nearly a factor of three on average.

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